Modified evolution of stellar binaries from supermassive black hole binaries

The evolution of main sequence binaries resided in the galactic centre is influenced a lot by the central super massive black hole (SMBH). Due to this perturbation, the stars in a dense environment are likely to experience mergers or collisions through secular or non-secular interactions. In this work, we study the dynamics of the stellar binaries at galactic center, perturbed by another distant SMBH. Geometrically, such a four-body system is supposed to be decomposed into the inner triple (SMBH-star-star) and the outer triple (SMBH-stellar binary-SMBH). We survey the parameter space and determine the criteria analytically for the stellar mergers and the tidal disruption events (TDEs). For a relative distant and equal masses SMBH binary, the stars have more opportunities to merge as a result from the Lidov-Kozai(LK) oscillations in the inner triple. With a sample of tight stellar binaries, our numerical experiments reveal that a significant fraction of the binaries, ~70 per cent, experience merger eventually. Whereas the majority of the stellar TDEs are likely to occur at a close periapses to the SMBH, induced by the outer Kozai effect. The tidal disruptions are found numerically as many as ~10 per cent for a close SMBH binary that is enhanced significantly than the one without the external SMBH. These effects require the outer perturber to have an inclined orbit (>=40 degree) relatively to the inner orbital plane and may lead to a burst of the extremely astronomical events associated with the detection of the SMBH binary.Comment: 12 pages, 9 figures, MNRAS in pres

Spinor Decomposition of SU(2) Gauge Potential and The Spinor Structures of Chern-Simons and Chern Density

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor structures, the knot quantum number of non-Abelian gauge theory is discussed, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping.Comment: 11 page